Thomas Aquinas embraces a controversial claim about the way in which parts of a substance depend on the substance’s substantial form. On his metaphysics, a ‘substantial form’ is not merely a relation among already existing things, in virtue of which (for example) the arrangement or configuration of those things would count as a substance. The substantial form is rather responsible for the identity or nature of the parts of the substance such a form constitutes. Aquinas’ controversial claim can be roughly (...) put as the view that things are members of their kind in virtue of their substantial form. To put it simply, Aquinas’ claim results in the implication that, every time the xs come to compose a y, those xs have to undergo a change in kind membership. -/- This has been called the “homonymy principle,” and it follows from Aquinas’ view of substantial forms, and specifically from the position that substantial forms inform prime matter, rather than substance-parts. The aim of this paper will be to defend that the Thomistic claim that substantial forms account for the determinate actuality of every part of a substance is plausible and coherent. After defending the Thomistic account, I propose that approaching problems of material composition as a Thomist has a significant, oft-overlooked advantage of involving a thorough-going naturalistic methodology that resolves such problems by appeal to empirical considerations. (shrink)
Aquinas’s characterization of sacra doctrina has received sustained engagement addressing its relation to contemporary conceptions of theology and Aristotelian conceptions of science. More recently, attention has been paid to Aquinas’s neo-Platonist influences, and the way they lead him to subvert purely Aristotelian categories. I therefore combine these themes by introducing the first study of whether sacra doctrina counts as a technê in Plato’s sense. After examining how Platonic technê relate to their ergon. epistasthai, gignôskein, and epistêmê and examining sacra doctrina’s (...) relationship to each of these Platonic categories, I suggest that sacra doctrina is an unqualified Platonic technê. (shrink)
In this book, philosopher Jean W. Rioux extends accounts of the Aristotelian philosophy of mathematics to what Thomas Aquinas was able to import from Aristotle’s notions of pure and applied mathematics, accompanied by his own original contributions to them. Rioux sets these accounts side-by-side modern and contemporary ones, comparing their strengths and weaknesses.
The authors explicate Aquinas's conception of mathematics. They show that in his work the Aristotelian conception is prevalent, according to which this discipline is—together with physics and metaphysics—a theoretical science, whose subject is the study of real quantity and its necessary properties. But, alongside this dominant and prevalent conception, Aquinas's work contains a number of indications that cast doubt. These sparse and rather marginal reflections lead the authors to conclude that Aquinas's texts contain a "constructivist" conception of mathematics in rudimentary (...) form. According to this approach, mathematics is not a theoretical science examining real quantity but, rather, a special kind of "art" by means of which mathematical objects are "created." From a constructivist point of view the authors then attempt to formulate a conception of mathematics that would accord with the basic Aristotelian assumptions of Aquinas's thought. (shrink)
This article examines one aspect of Thomas Aquinas' understanding of abstraction. It shows in which way, according to Aquinas, universal material objects and individual material objects are the starting point for mathematical objects. It comes to the conclusion that for Aquinas there are not only universal mathematical objects (circle, line), but also individual mathematical objects (this circle, that line). Universal mathematical objects are properties of universal material objects and individual mathematical objects are properties of individual material objects. One type of (...) abstractio formae leads from individual material objects to universal mathematical objects, a second type from universal material objects to universal mathematical objects, and a third type from individual material objects to individual mathematical objects. Therefore, the concept of abstractio formae is ambiguous. (shrink)